Expression of type Forall

from the theory of proveit.numbers.numerals.decimals

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import a, n
from proveit.core_expr_types import b_1_to_n
from proveit.logic import Forall, InSet
from proveit.numbers import DecimalSequence, Digits, Natural, NaturalPos, greater, zero

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [a, b_1_to_n], instance_expr = InSet(DecimalSequence(a, b_1_to_n), NaturalPos), domain = Digits, condition = greater(a, zero)), domain = Natural)

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{n \in \mathbb{N}}~\left[\forall_{a, b_{1}, b_{2}, \ldots, b_{n} \in \mathbb{N}^{\leq 9}~|~a > 0}~\left(\texttt{\#}(a ~ b_{1}, b_{2}, \ldots, b_{n}) \in \mathbb{N}^+\right)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 35 body: 4
3	ExprTuple	35
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 36 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	35, 11
10	Lambda	parameters: 24 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 36 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21, 22
18	Operation	operator: 23 operands: 24
19	Literal
20	Operation	operator: 36 operands: 25
21	ExprRange	lambda_map: 26 start_index: 34 end_index: 35
22	Operation	operator: 27 operands: 28
23	Literal
24	ExprTuple	32, 29
25	ExprTuple	32, 39
26	Lambda	parameter: 42 body: 30
27	Literal
28	ExprTuple	31, 32
29	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
30	Operation	operator: 36 operands: 37
31	Literal
32	Variable
33	Lambda	parameter: 42 body: 38
34	Literal
35	Variable
36	Literal
37	ExprTuple	38, 39
38	IndexedVar	variable: 40 index: 42
39	Literal
40	Variable
41	ExprTuple	42
42	Variable